On the practical global uniform asymptotic stability of stochastic differential equations

The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, in particular, of stochastic differential systems. The main purpose of the paper is the analysis of the stability of stochastic differential equations (SDEs) by using Lyapunov functions when the origin is not necessarily an equilibrium point. The global uniform boundedness and the global practical uniform exponential stability of solutions of SDEs based on Lyapunov techniques are investigated. Furthermore, an example is given to illustrate the applicability of the main result.     

关于经济波动周期性及成因的实证研究

经济波动是经济发展过程中的常见现象。本文首先用两种方法分析了改革开放以来我国经济的波动状态,接着用数理统计方法对其周期性进行了检验,在此基础上作者又从两个角度分析了改革以来我国经济周期波动的形成原因。     

Attitudes and preferences: Approaches to representing decision maker desires

Informative interrelationships between attitudes and preferences when formally studying a conflict within the framework of the Graph Model for Conflict Resolution are specified through the development of formal theorems. Specifically, the parallel nature of attitudes and preferences is illuminated to show how attitudes can provide a simple way to more effectively represent complex preference structures when decision makers hold concern for other decision makers’ interests. To illustrate this important property of attitudes, the Graph Model for Conflict Resolution is applied to the negotiation over the sale of a brownfield property both with and without attitudes.     

Complex calculators in the classroom: theoretical and practical reflections on teaching pre-calculus

University and older school students following scientific courses now use complex calculators with graphical, numerical and symbolic capabilities. In this context, the design of lessons for 11th grade pre-calculus students was a stimulating challenge.In the design of lessons, emphasising the role of mediation of calculators and the development of schemes of use in an 'instrumental genesis' was productive. Techniques, often discarded in teaching with technology, were viewed as a means to connect task to theories. Teaching techniques of use of a complex calculator in relation with 'traditional' techniques was considered to help students to develop instrumental and paper/pencil schemes, rich in mathematical meanings and to give sense to symbolic calculations as well as graphical and numerical approaches.The paper looks at tasks and techniques to help students to develop an appropriate instrumental genesis for algebra and functions, and to prepare for calculus. It then focuses on the potential of the calculator for connecting enactive representations and theoretical calculus. Finally, it looks at strategies to help students to experiment with symbolic concepts in calculus.This revised version was published online in September 2005 with corrections to the Cover Date.     

关于Nielson Zeta函数的有理性

Ａ．Ｌ．Ｆｅｌ＇ｓｈｔｙｎ和Ｖ．Ｂ．Ｐｉｌｙｕｇｉｎａ定义了Ｎｉｅｌｓｏｎｚｅｔａ函数并证明关于其有理性的一些结果，本文改进了他们的一些结果。     

Robust semiglobally practical stabilization for nonlinear singularly perturbed systems

In this work, the problem of semiglobally practical stabilization is considered for nonlinear singularly perturbed systems with unknown parameters. The composite Lyapunov function for the full systems is established by both that of the slow subsystem and the boundary layer system. A state feedback control law for the linear part of the slow subsystem and boundary layer system is proposed which renders the whole closed-loop system semiglobally stable. The upper bound expression of ε$\epsilon$ is given to obtain the condition of asymptotic stability for the system. A simulation example is given to demonstrate the effectiveness and feasibility of the controller.     

关于良定问题

本文应用有限理性模型M,对非线性问题的良定性进行了统一的研究,对最优化、多目标最优化、非合作博弈和广义博弈得到了一些新的良定性结果.     

On the practical value of the notion ofBN-stability

The oldest concept of unconditional stability of numerical integration methods for ordinary differential systems is that ofA-stability. This concept is related to linear systems having constant coefficients and has been introduced by Dahlquist in 1963. More recently, since another contribution of Dahlquist in 1975, there has been much interest in unconditional stability properties of numerical integration methods when applied to non-linear dissipative systems (G-stability,BN-stability,A-contractivity). Various classes of implicit Runge-Kutta methods have already been shown to beBN-stable. However, contrary to the property ofA-stability, when implementing such a method for practical use this unconditional stability property may be lost. The present note clarifies this for a class of diagonally implicit methods and shows at the same time that Rosenbrock's method is notBN-stable.     

On based-free actions of compact lie groups on the hilbert cube

It is proved that a based-free action α of a given compact Lie groupG on the Hilbert cubeQ is equivalent to the standard based-free action σ if and only if the orbit spaceQ ₀/α of the free partQ ₀=Q* is aQ-manifold having the proper homotopy type of the orbit spaceQ ₀/σ. The existence of an equivariant retraction (Q ₀, σ)→(Q ₀, α) is established. It is proved that for any TikhonovG-spaceX the family of all equivariant mapsX→ conG separates the points and the closed sets inX. Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 163–174, February, 1999.     

模糊选择函数T-拟传递合理性充要条件的研究

T-拟传递合理性对模糊选择函数的研究至关重要.基于选择集为正规模糊选择集,对任意的t-模,利用文献中已有的结论,深入研究了模糊选择函数T-拟传递合理性的刻画问题,得到了模糊选择函数T-拟传递合理性的充要条件.     

基于序列稳定性的冲突当局者行为分析模型

不同稳定性可以折射冲突当局者的不同行为类型,为了更全面且深入地了解当局者的行为类型,本文将现有四种基本稳定性拓展至六种,构建了一个能够提高冲突分析图模型理论普遍实用性的决策方法。首先,提出了强、弱序列稳定性(SEQ稳定)的逻辑概念,以此分析当局者具有不同程度的过度自信下的冲突决策过程。然后,定义了强、弱SEQ稳定的矩阵表达,以此促进相应稳定解的计算和编程算法的实现。最后,使用“制造商与零售商渠道价格冲突”案例说明强弱SEQ稳定的意义。研究发现:冲突当局者的过度自信偏差并不都会产生负面影响,有时会利于当局者的集体利益。     

关于群胚作用和李双代数胚态射

在这篇文章中，我们讨论了李双代数胚之间的态射，得到了一些李双代数胚之间态射的性质．研究了泊松群胚在泊松流形上的泊松作用，以及这个泊松作用与被作用流形的切李双代数胚到作用泊松群胚的切李双代数胚之间的态射的关系，得到了一些有用的结论。     

On the practical application of the modified romberg algorithm

Experience gained in the use of the modified Romberg algorithm is reported. An alternative form of the algorithm based on a cosine transformation of Euler-MacLaurin's and Euler's second formula is discussed. Some examples where the error estimate incorporated in the algorithm partly fails are given. Finally an ALGOL procedure combining the algorithm discussed in a previous paper of the author [1] and the modification discussed in this paper is described.     

On Method Overfitting

Benchmark problems should be hard. True. Methods for solving problems should be useful for more than just beating a particular benchmark. Truer still, we believe. In this paper, we examine the worthiness of the approach consisting of concentration on a particular set of benchmark problems, an issue raised by a recent paper by Ian Gent. We find that such a methodology can easily lead to publications of limited general use as far as our ability to solve practical problems is concerned.     

"常微分方程"课程建设探讨

根据常微分方程课程特点及常微分方程的发展,探讨了常微分方程精品课程建设中师资队伍建设和教材改革与建设的重要性,提出了对改革有关教学内容以及编写具有本课程特色的优秀教材的具体设想.     

On a Group Acting Locally Freely on an Abelian Group

A group acting on an abelian group is finite provided that it is generated by a class of conjugate elements such that every two elements of the class generate a finite subgroup that acts freely.     

On the uniqueness of overcomplete dictionaries, and a practical way to retrieve them

A full-rank under-determined linear system of equations Ax = b has in general infinitely many possible solutions. In recent years there is a growing interest in the sparsest solution of this equation—the one with the fewest non-zero entries, measured by ∥x∥₀. Such solutions find applications in signal and image processing, where the topic is typically referred to as “sparse representation”. Considering the columns of A as atoms of a dictionary, it is assumed that a given signal b is a linear composition of few such atoms. Recent work established that if the desired solution x is sparse enough, uniqueness of such a result is guaranteed. Also, pursuit algorithms, approximation solvers for the above problem, are guaranteed to succeed in finding this solution.Armed with these recent results, the problem can be reversed, and formed as an implied matrix factorization problem: Given a set of vectors {b_i}, known to emerge from such sparse constructions, Ax_i = b_i, with sufficiently sparse representations x_i, we seek the matrix A. In this paper we present both theoretical and algorithmic studies of this problem. We establish the uniqueness of the dictionary A, depending on the quantity and nature of the set {b_i}, and the sparsity of {x_i}. We also describe a recently developed algorithm, the K-SVD, that practically find the matrix A, in a manner similar to the K-Means algorithm. Finally, we demonstrate this algorithm on several stylized applications in image processing.     

On the Stability of Diagonal Actions

In the note it is proved that, for an arbitrary action of a semisimple group G on an affine variety X, there is a positive integer n such that the diagonal action (m copies) is stable for any .     

ON THE CONSTRUCTION AND ENUMERATION OF HAMILTONIAN GRAPHS

In this paer we give a farmula for enumerating the equivalent classes of orderly labeled Hamiltonian graphs under group D.and two algorithms for constructing these equivalent classes and all nonisomorphic Hamiltonian graphs.Some computational results obtained by microcomputers are listed.     

Convergence of aspirations and (partial) cooperation in the prisoner's dilemma

This paper proposes an aspiration-based dynamic model for cooperation where a large population of agents are matched afresh every period to play a Prisoner's Dilemma. At each point in time, agents hold a common aspiration level which is updated on the basis of some “population statistic”, i.e. a certain scalar summary (e.g. average payoff) associated to the current state. On the other hand, those agents who feel “dissatisfied” (relative to current aspiration) switch actions at a rate which is increasing in the magnitude of the dissatisfaction. The resulting process is shown to converge in the long run under quite general conditions. Moreover, if agents are responsive enough, the long-run social state displays some extent of cooperation, with a constant positive fraction of the population (always less than half) choosing to cooperate in every period. Received: January 1998/Revised version: October 1998